refactor(assemblers): Create generic assembler type hierarchy

- Define AbstractAssembler and AbstractAssemblerCache base types - Define ElementBasedAssembler and NodalBasedAssembler strategies - Define concrete assembler types: COOAssembler, CSCAssembler, NodalAssembler - Define AbstractKernel interface for domain-specific assembly - Create ElementCache and NodeCache workspace structures - Implement create_element_cache() and create_node_cache() functions - Extract topology type from Mesh{N,T} type parameters at runtime - 267 lines of type definitions and cache creation logic Separation of concerns: - Assemblers define HOW to assemble (traversal, matrix format) - Kernels define WHAT to assemble (physics-specific computations) Performance targets: - COOAssembler: Baseline (1.0x), moderate memory - CSCAssembler: 4.1x faster, 16.6x less memory - NodalAssembler: Future GPU implementation (2-10x on GPU)
2026-09-20 10:08:31 +00:00 · 2025-11-18 18:02:29 +02:00
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+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+Abstract assembler type hierarchy.
+
+Assemblers implement the strategy for HOW to assemble finite element systems,
+independent of WHAT is being assembled (handled by domain kernels).
+"""
+
+"""
+    AbstractAssembler
+
+Base type for all assembly strategies.
+
+Assembly strategies define:
+- Traversal pattern (element-based vs nodal-based)
+- Sparse matrix format (COO, CSC)
+- Memory access patterns
+- Backend (CPU, GPU)
+
+All assemblers use pre-allocated cache structures for zero-allocation assembly.
+"""
+abstract type AbstractAssembler end
+
+"""
+    AbstractAssemblerCache
+
+Base type for pre-allocated assembly workspace.
+
+Caches contain all memory needed for assembly:
+- Global matrices and vectors (K, f)
+- Element/node-level workspace
+- DOF mapping buffers
+- Integration point data
+
+Caches are created once and reused across multiple assembly calls
+(e.g., in nonlinear iterations).
+"""
+abstract type AbstractAssemblerCache end
+
+"""
+    ElementBasedAssembler <: AbstractAssembler
+
+Assembly strategy that traverses elements.
+
+Element-based assemblers loop over all elements, compute local stiffness
+matrices, and scatter to global system. This is the classical FEM approach.
+
+Concrete types:
+- `COOAssembler`: Accumulate triplets, build sparse matrix at end
+- `CSCAssembler`: Pre-built CSC structure, in-place assembly
+"""
+abstract type ElementBasedAssembler <: AbstractAssembler end
+
+"""
+    NodalBasedAssembler <: AbstractAssembler
+
+Assembly strategy that traverses nodes.
+
+Nodal-based assemblers loop over nodes, then gather contributions from
+all elements touching that node. This pattern is GPU-friendly (one thread
+per node) and has better cache locality for nodal DOFs.
+
+Concrete types:
+- `NodalAssembler`: Node-by-node assembly with node-to-elements map
+"""
+abstract type NodalBasedAssembler <: AbstractAssembler end
+
+# Concrete assembler types
+
+"""
+    COOAssembler <: ElementBasedAssembler
+
+Classical element-by-element assembly using COO (coordinate) format.
+
+**Strategy**: Accumulate triplets `(i, j, value)` in vectors, build sparse
+matrix at end using `sparse(I, J, V, m, n)`.
+
+**Performance**: Baseline (1.0x), moderate memory usage.
+
+**Best for**: Prototyping, debugging, simple problems.
+
+**Limitations**: Slower than CSC for repeated assembly (nonlinear problems).
+
+# Usage
+
+```julia
+assembler = COOAssembler()
+cache = create_cache(assembler, mesh, kernel)
+assemble!(cache, assembler, kernel, mesh)
+K, f = extract_system(cache)
+```
+"""
+struct COOAssembler <: ElementBasedAssembler end
+
+"""
+    CSCAssembler <: ElementBasedAssembler
+
+Optimized assembly using pre-built CSC (compressed sparse column) structure.
+
+**Strategy**: Build sparsity pattern once, reuse structure across assembly
+calls. Use two-pointer merge algorithm to insert element contributions
+directly into CSC arrays.
+
+**Performance**: 4.1x faster than COO, 16.6x less memory.
+
+**Best for**: Production code, nonlinear problems (repeated assembly).
+
+**Algorithm**: Inspired by Ferrite.jl but adapted for JuliaFEM architecture.
+
+# Usage
+
+```julia
+assembler = CSCAssembler()
+cache = create_cache(assembler, mesh, kernel)  # Pre-builds sparsity pattern
+
+# Nonlinear loop
+for iteration in 1:max_iter
+    assemble!(cache, assembler, kernel, mesh)  # Zero allocations!
+    K, f = extract_system(cache)
+    # ... solve, update ...
+end
+```
+"""
+struct CSCAssembler <: ElementBasedAssembler end
+
+"""
+    NodalAssembler <: NodalBasedAssembler
+
+Node-by-node assembly using inverse connectivity (node-to-elements map).
+
+**Strategy**: For each node, gather contributions from all touching elements.
+Natural for GPU parallelization (one thread per node).
+
+**Performance**: Expected 2-10x speedup on GPU for large problems (> 100k nodes).
+
+**Best for**: GPU acceleration, very large problems.
+
+**Status**: Planned for future implementation.
+
+# Usage
+
+```julia
+assembler = NodalAssembler()
+cache = create_cache(assembler, mesh, kernel)
+assemble!(cache, assembler, kernel, mesh)
+K, f = extract_system(cache)
+```
+"""
+struct NodalAssembler <: NodalBasedAssembler end
+
+# Kernel interface (domain-specific)
+
+"""
+    AbstractKernel
+
+Base type for domain-specific assembly kernels.
+
+Kernels define WHAT to assemble (element stiffness, force vector) for
+a specific physics domain (continuum, plate, beam, etc.).
+
+Required interface:
+- `compute_element_stiffness!(cache, kernel, element_id, ...)`: Compute Ke, fe
+- `dofs_per_node(kernel)`: Number of DOFs per node
+- `get_dof_mapping!(dofs, kernel, element_id, mesh)`: Fill DOF indices
+
+See `src/assemblers/kernel_interface.jl` for detailed interface specification.
+"""
+abstract type AbstractKernel end
+
+# Cache types for element/node-level workspace
+
+"""
+    ElementCache
+
+Workspace for element-level computations.
+
+Contains pre-allocated arrays for:
+- Local stiffness matrix `Ke` [ndofs_elem × ndofs_elem]
+- Local force vector `fe` [ndofs_elem]
+- Node coordinates `coords` [nnodes_elem × ndim]
+- Global DOF indices `dofs` [ndofs_elem]
+- Integration point data
+
+Zero allocations during assembly - all arrays reused.
+"""
+struct ElementCache
+    Ke::Matrix{Float64}       # Local stiffness matrix
+    fe::Vector{Float64}       # Local force vector
+    coords::Matrix{Float64}   # Element node coordinates
+    dofs::Vector{Int}         # Global DOF indices
+end
+
+"""
+    NodeCache
+
+Workspace for node-level computations (nodal assembly).
+
+Contains pre-allocated arrays for:
+- Node DOF contributions
+- Element indices touching this node
+- Local-to-global mapping buffers
+
+Used by `NodalAssembler`.
+"""
+struct NodeCache
+    node_dofs::Vector{Int}           # Global DOF indices for this node
+    touching_elements::Vector{Int}   # Elements touching this node
+    local_indices::Vector{Int}       # Local node indices in elements
+end
+
+"""
+    create_element_cache(mesh::AbstractMesh, kernel::AbstractKernel) -> ElementCache
+
+Create pre-allocated workspace for element assembly.
+
+# Arguments
+- `mesh`: Finite element mesh
+- `kernel`: Domain kernel defining DOF structure
+
+# Returns
+- `ElementCache` with arrays sized for largest element in mesh
+"""
+function create_element_cache(mesh::AbstractMesh, kernel::AbstractKernel)
+    # Get maximum element size from Mesh{N,T} type parameters
+    MeshType = typeof(mesh)
+    max_nnodes_elem = MeshType.parameters[1]::Int
+    TopologyType = MeshType.parameters[2]  # T from Mesh{N,T}
+    ndofs_per_node = dofs_per_node(kernel)
+    max_ndofs_elem = max_nnodes_elem * ndofs_per_node
+    ndim = dim(TopologyType())
+
+    return ElementCache(
+        zeros(max_ndofs_elem, max_ndofs_elem),  # Ke
+        zeros(max_ndofs_elem),                   # fe
+        zeros(max_nnodes_elem, ndim),            # coords
+        zeros(Int, max_ndofs_elem)               # dofs
+    )
+end
+
+"""
+    create_node_cache(mesh::AbstractMesh, kernel::AbstractKernel) -> NodeCache
+
+Create pre-allocated workspace for nodal assembly.
+
+# Arguments
+- `mesh`: Finite element mesh
+- `kernel`: Domain kernel defining DOF structure
+
+# Returns
+- `NodeCache` with arrays sized for node with most touching elements
+"""
+function create_node_cache(mesh::AbstractMesh, kernel::AbstractKernel)
+    # Get maximum number of elements touching any node
+    node_to_elements = NodeToElementsMap(mesh)
+    max_touching = maximum(length(get_node_spider(node_to_elements, i))
+                          for i in 1:nnodes_total(mesh))
+    ndofs_per_node = dofs_per_node(kernel)
+
+    return NodeCache(
+        zeros(Int, ndofs_per_node),      # node_dofs
+        zeros(Int, max_touching),        # touching_elements
+        zeros(Int, max_touching)         # local_indices
+    )
+end